2024 AMC 8 Problems
2024 AMC 8 (Answer Key) Printable versions: • AoPS Resources • PDF | ||
Instructions
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==Problem 1== One behalf of the AoPS team we have came to notice that these questions are editable as our dev team in on break at the moment this bug will not be fixed. Everyone who has written something no matter what the reason has broken the code of conduct witch was signed in the creation of your account. By writing something here your account will be banned(In the next 48 hours) and you will be banned from taking any future AoPS competitions. Our team here at AoPS has also came to notice that the AMC-8 2024 answers have been leaked as this is changing the results all over the country we will not be counting this test and will be creating another one to take its place. We have also noticed that there is one individual trying to stop the cheating of AMC-8 and thank you for including some light hearted jokes to help lighten the mood. On the behalf of the AoPS team we thank you for reading this message.
Contents
Problem 2
One behalf of the AoPS team we have came to notice that these questions are editable as our dev team in on break at the moment this bug will not be fixed. Everyone who has written something no matter what the reason has broken the code of conduct witch was signed in the creation of your account. By writing something here your account will be banned(In the next 48 hours) and you will be banned from taking any future AoPS competitions. Our team here at AoPS has also came to notice that the AMC-8 2024 answers have been leaked as this is changing the results all over the country we will not be counting this test and will be creating another one to take its place. We have also noticed that there is one individual trying to stop the cheating of AMC-8 and thank you for including some light hearted jokes to help lighten the mood. On the behalf of the AoPS team we thank you for reading this message.
Problem 6
4 random points are chosen on a sphere. What is the probability that the tetrahedron with vertices of the 4 points contains the center of the sphere?
(A) 1/2 (B) 1/4 (C) 3/8 (D) 1/8 (E) 3/10 (Source: Putnam) lmao
Problem 8
Bob has a magical nuclear button that will explode one out of the 12,500 nukes on our planet. One nuke is called the "Tsar Bomb". At random, what is the chance that Bob will explode the Tsar Bomba after detonating another special nuke called "OPO"?
(A) 1/12500 (B) People will die (C) The FBI will come (D) you don't know (E) you want to cheat for the AMC8 (F) you want to know how many problems you got correct on the AMC 8 (G) you think problem 15 would be really fun to solve (I) you looked at problem 15 (J) you didn't realize I skipped option H
Problem 9
If you are canoeing down a road, and a tire falls off, how many pancakes do you need to build a doghouse?
(A) 34 (C) purple (B) teaspoon (D) penguin (E)
Problem 4
What is the sum of the roots of
?
A)0 B)-1 C)1 D)-2 E)2
Problem 11
The equation (2^(333x-2))+(2^(111x+2))=(2^(222x+1))+1 has three real roots. Find their sum. (Source: AIME)
(A) 4/113 (B) 2/111 (C) 6/11 (D) 5/111 (E) 14/113
You thought we could let you cheat?
Problem 12
Assuming that , then what does
equal?
Problem 13
A finite set of positive integers has the property that, for each
, and each positive integer divisor
of
, there exists a unique element
satisfying
(the elements
and
could be equal).
Given this information, find all possible values for the number of elements of . (source: 2021 USAMO)
now that you read this problem you have to do it without looking at the solution or else... let's just say bad things will happen
Problem 14
Let k >/ 2 be an integer. Find the smallest integer >/ k + 1 with the property that
there exists a set of n distinct real numbers such that each of its elements can be written as a
sum of k other distinct elements of the set. (Source: IMO Shortlist Slovakia)
(A) + 3 (B)
- 3 (C)
+ 4 (D)
(E)
+ 5
Problem 15
Let be an interior point of the acute triangle
with
so that
. The point
on the segment
satisfies
, the point
on the segment
satisfies
, and the point
on the line
satisfies
. Let
and
be the circumcentres of the triangles
and
respectively. Prove that the lines
,
, and
are concurrent. (source: 2021 IMO)
now go do this problem WITHOUT THE SOLUTION as a punishment for trying to cheat
What is the value of 1, assuming that 1=1, but 1= 3(4x^2-7x+5) - 2(5x^2-9x-3)=6x
Problem 17
Let. Compute the last three digits of
.
NO CALCULATORS ARE ALLOWED.
Try this.
Problem 18
hi guys. trying to cheat? im ashamed of you code: nsb
Problem 19
Write your AoPS name here if you took the AMC 8.
Probablity NapoleonicAviator Multpi12 funbeast mathkindacool_ Rainier2020
Problem 20
Find the sum of the square root of -2 and the last digit of pi.
Problem 21
what is 9+10?
(A) 21 (B) 69 (C) 19 (D) nothing (E) something
Problem 22
What is the sum of the cubes of the solutions cubed of ?
(A) 1 (B) 8 (C) 27 (D) -1 (E) -27
Problem 23
lol we are the defenders against the cheaters... get outta here and study
SubText: and im here writing soulutions for these joke problems. (Multpi12)
And so am I ;)
Problem 24
wait when are the questions coming tho I think it's 1/25 for official answers since all tests end at 1/24
Problem 25
If Bob is travelling at the speed of 3 George Washington, how long will it take for him to finish his chutney.
A) 13 Hours B) 7 minute C) NA D) 12 Neptunes E) IDK
See Also
2024 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by 2023 AMC 8 |
Followed by 2025 AMC 8 | |
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All AJHSME/AMC 8 Problems and Solutions |